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Abstract Submarine melting at Greenland's marine terminating glaciers is a crucial, yet poorly constrained process in the coupled ice‐ocean system. Application of Antarctic melt rate representations, derived for floating glacier tongues, to non‐floating marine terminating glaciers commonly found in Greenland, results in a dramatic underestimation of submarine melting. Here, we revisit the physical theory underlying melt rate parameterizations and leverage recently published observational data to derive a novel melt rate parameterization. This is the first parameterization that (a) consistently comprises both convective‐ and shear‐dominated melt regimes, (b) includes coefficients quantitatively constrained using observational data, and (c) is applicable to any vertical glacier front. We show that, compared to the current state‐of‐the‐art approach, the scheme provides an improved fit to observed melt rates on the scale of the terminating front, offering an opportunity to incorporate this critical missing forcing into ocean circulation models. 

Abstract Ocean observations are expensive and difficult to collect. Designing effective ocean observing systems therefore warrants deliberate, quantitative strategies. We leverage adjoint modeling and Hessian uncertainty quantification (UQ) within the ECCO (Estimating the Circulation and Climate of the Ocean) framework to explore a new design strategy for ocean climate observing systems. Within this context, an observing system is optimal if it minimizes uncertainty in a set of investigator‐defined quantities of interest (QoIs), such as oceanic transports or other key climate indices. We show that Hessian UQ unifies three design concepts. (1) An observing system reduces uncertainty in a target QoI most effectively when it is sensitive to the same dynamical controls as the QoI. The dynamical controls are exposed by the Hessian eigenvector patterns of the model‐data misfit function. (2) Orthogonality of the Hessian eigenvectors rigorously accounts for redundancy between distinct members of the observing system. (3) The Hessian eigenvalues determine the overall effectiveness of the observing system, and are controlled by the sensitivity‐to‐noise ratio of the observational assets (analogous to the statistical signal‐to‐noise ratio). We illustrate Hessian UQ and its three underlying concepts in a North Atlantic case study. Sea surface temperature observations inform mainly local air‐sea fluxes. In contrast, subsurface temperature observations reduce uncertainty over basin‐wide scales, and can therefore inform transport QoIs at great distances. This research provides insight into the design of effective observing systems that maximally inform the target QoIs, while being complementary to the existing observational database. 

Abstract A number of feedbacks regulate the response of Arctic sea ice to local atmospheric warming. Using a realistic coupled ocean‐sea ice model and its adjoint, we isolate a mechanism by which significant ice growth at the end of the melt season may occur as a lagged response to Arctic atmospheric warming. A series of perturbation simulations informed by adjoint model‐derived sensitivity patterns reveal the enhanced ice growth to be accompanied by a reduction of snow thickness on the ice pack. Detailed analysis of ocean‐ice‐snow heat budgets confirms the essential role of the reduced snow thickness for persistence and delayed overshoot of ice growth. The underlying mechanism is a snow‐melt‐conductivity feedback, wherein atmosphere‐driven snow melt leads to a larger conductive ocean heat loss through the overlying ice layer. Our results highlight the need for accurate observations of snow thickness to constrain climate models and to initialize sea ice forecasts. 

Abstract Oceanic quantities of interest (QoIs), for example, ocean heat content or transports, are often inaccessible to direct observation, due to the high cost of instrument deployment and logistical challenges. Therefore, oceanographers seek proxies for undersampled or unobserved QoIs. Conventionally, proxy potential is assessed via statistical correlations, which measure covariability without establishing causality. This paper introduces an alternative method: quantifying dynamical proxy potential. Using an adjoint model, this method unambiguously identifies the physical origins of covariability. A North Atlantic case study illustrates our method within the ECCO (Estimating the Circulation and Climate of the Ocean) state estimation framework. We find that wind forcing along the eastern and northern boundaries of the Atlantic drives a basin‐wide response in North Atlantic circulation and temperature. Due to these large‐scale teleconnections, a single subsurface temperature observation in the Irminger Sea informs heat transport across the remote Iceland‐Scotland ridge (ISR), with a dynamical proxy potential of 19%. Dynamical proxy potential allows two equivalent interpretations: Irminger Sea subsurface temperature (i) shares 19% of its adjustment physics with ISR heat transport and (ii) reduces the uncertainty in ISR heat transport by 19% (independent of the measured temperature value), if the Irminger Sea observation is added without noise to the ECCO state estimate. With its two interpretations, dynamical proxy potential is simultaneously rooted in (i) ocean dynamics and (ii) uncertainty quantification and optimal observing system design, the latter being an emerging branch in computational science. The new method may therefore foster dynamics‐based, quantitative ocean observing system design in the coming years. 

Abstract The lack of continuous spatial and temporal sampling of hydrographic measurements in large parts of the Arctic Ocean remains a major obstacle for quantifying mean state and variability of the Arctic Ocean circulation. This shortcoming motivates an assessment of the utility of Argo-type floats, the challenges of deploying such floats due to the presence of sea ice, and the implications of extended times of no surfacing on hydrographic inferences. Within the framework of an Arctic coupled ocean–sea ice state estimate that is constrained to available satellite and in situ observations, we establish metrics for quantifying the usefulness of such floats. The likelihood of float surfacing strongly correlates with the annual sea ice minimum cover. Within the float lifetime of 4–5 years, surfacing frequency ranges from 10–100 days in seasonally sea ice–covered regions to 1–3 years in multiyear sea ice–covered regions. The longer the float drifts under ice without surfacing, the larger the uncertainty in its position, which translates into larger uncertainties in hydrographic measurements. Below the mixed layer, especially in the western Arctic, normalized errors remain below 1, suggesting that measurements along a path whose only known positions are the beginning and end points can help constrain numerical models and reduce hydrographic uncertainties. The error assessment presented is a first step in the development of quantitative methods for guiding the design of observing networks. These results can and should be used to inform a float network design with suggested locations of float deployment and associated expected hydrographic uncertainties.